The M-estimator in a multi-phase random nonlinear model

We consider a multi-phase random regression model, discontinuous in each change-point, with an arbitrary error $\epsilon$. In the case that the number of jumps is known, the M-estimator for the locations of the jumps and for the coefficient parameters are studied. These estimators are consistent and the distribution for the estimators of the coefficients is Gaussian. The estimators of the change-points converge, with the rate $n^{-1}$, to the smallest minimizer of the independent compound Poisson processes.